Cox Proportional Hazards Model

Introduction to Cox Proportional Hazards Model

• Developed by Sir David R. Cox in 1972
• Statistical method for survival analysis and epidemiological research
• Analyzes time-to-event data
• Estimates hazard function
• Explores relationships with independent variables
• Applications include healthcare, engineering, social sciences

Methods

• Semiparametric survival analysis method
• Right-censored data \[ λ(t) = λ0(t) * exp(β₁X₁ + β₂X₂ + ... + βₖ) \]

Assumptions/Limitations

• Proportional Hazard Assumption
• Linearity of Continuous Variables
• Independence of Censoring
• Sensitivity to Outliers

Data Description

• National Cancer Institute Surveillance, Epidemiology, and End Results Program (SEER)
• Comprehensive cancer surveillance system in the US
• Covers a wide range of demographic information
• Provides insights into cancer trends, outcomes, and risk factors at a national level

Data Table

Data Visualization

Objective and Purpose

• Explore factors impacting patient survival
• Analyze key variables such as cancer type, race, gender, age
• Understanding their significance in predicting survival
• Assess hazard ratios for each variable
• Center analysis on relationships and impact on survival outcomes

Statistical Modeling for Data

Stratified Analysis

Adding an Interaction term to Filtered Analysis on Deceased Patients

Data Analysis with Reference Categories

Model with Time-Dependent Covariates

Conclusion

• Identified key predictors impacting cancer survival
• Explored survival dynamics
• Proportional Hazards assumption violated
• Stratification, Interaction Term, Time-Dependent covariates

References